Multiplier ideals, 𝑉-filtration, and spectrum

Budur, Nero; Saito, Morihiko

doi:10.1090/S1056-3911-04-00398-4

Multiplier ideals, $V$-filtration, and spectrum

Authors: Nero Budur and Morihiko Saito
Journal: J. Algebraic Geom. 14 (2005), 269-282
DOI: https://doi.org/10.1090/S1056-3911-04-00398-4
Published electronically: December 9, 2004
MathSciNet review: 2123230
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Abstract | References | Additional Information

Abstract: For an effective divisor on a smooth algebraic variety or a complex manifold, we show that the associated multiplier ideals coincide essentially with the filtration induced by the filtration $V$ constructed by B. Malgrange and M. Kashiwara. This implies another proof of a theorem of L. Ein, R. Lazarsfeld, K.E. Smith, and D. Varolin that any jumping coefficient in the interval $(0,1]$ is a root of the Bernstein-Sato polynomial up to sign. We also give a refinement (using mixed Hodge modules) of the formula for the coefficients of the spectrum for exponents not greater than one or greater than the dimension of the variety minus one.

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Additional Information

Nero Budur
Affiliation: Department of Mathematics, University of Illinois at Chicago, 851 South Morgan Street (M/C 249), Chicago, Illinois 60607-7045
Address at time of publication: Department of Mathematics, Johns Hopkins University, Baltimore, Maryland 21218
Email: nero@math.uic.edu, nbudur@math.jhu.edu

Morihiko Saito
Affiliation: RIMS Kyoto University, Kyoto 606-8502 Japan
Email: msaito@kurims.kyoto-u.ac.jp

Received by editor(s): June 15, 2003
Published electronically: December 9, 2004